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**Global asymptotic stability of 3-species mutualism models with diffusion and delay effects.**
*(English)*
Zbl 1179.35332

Summary: In this paper, the Lotka-Volterra 3-species mutualism models with diffusion and delay effects is investigated. A simple and easily verifiable condition is given to ensure the global asymptotic stability of the unique positive steady-state solution of the corresponding steady-state problem in a bounded domain with Neumann boundary condition. Our approach to the problem is based on inequality skill and the method of the upper and lower solutions for a more general reaction-diffusion system. Finally, some numerical simulations are given to illustrate our results.

### MSC:

35Q92 | PDEs in connection with biology, chemistry and other natural sciences |

92D25 | Population dynamics (general) |

35B35 | Stability in context of PDEs |

35B40 | Asymptotic behavior of solutions to PDEs |

35A15 | Variational methods applied to PDEs |

### Keywords:

Lotka-Volterra 3-species mutualism models; diffusion and delay effects; global asymptotic stability; upper and lower solutions
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\textit{C.-Y. Wang} et al., Discrete Dyn. Nat. Soc. 2009, Article ID 317298, 20 p. (2009; Zbl 1179.35332)

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